Gel electrophoresis is a widely used technique to separate polymers. It has great importance in modern molecular biology as a method for separating and analyzing proteins and nucleic acids, in particular DNA. In its simplest form, the technique consists of applying a constant electric field to a gel that contains the molecules of interest. The difference in mobility of the molecules causes them to migrate differently and hence to separate physically in the gel after a period of time. At low electric fields, the mobility of linear polymers is inversely dependent on chain molecular weigh At higher fields nonlinear effects strongly reduce the mobility dependence on the molecular weight resulting in the inability to separate the chains. In an effort to optimize the separation process, more sophisticated approaches have been developed. Despite its importance, there is still no physical understanding of the way polymers behave under the influence of an electric field in an entangled medium. Experimental developments have relied solely on empirical observations. In order to understand the dynamics of gel electrophoresis, an off lattice computer simulation of the process has been developed. The simulation will provide information of the internal motion of the chain which is needed to optimize the separation technique. We will determine the characteristic diffusion of the center of mass and the monomers as well as the polymer conformation as a function of time. The dynamical quantities to be computed will be analyzed as a function of chain molecular weight; pore size of the gel and field strength. In addition, gel electrophoresis of circular molecules of various topologies will be studied by computer simulations. In particular gel electrophoresis of configurations occurring in closed circular DNA will be analyzed. The results of these studies will be used to optimize gel electrophoresis as a separation process.